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OF  ILLINOIS 

LIBRARY 


aeRlCULTURAL 
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UNIVERSITY  OF  ILLINOIS 

Agricultural  Experiment  Station 


BULLETIN  No.  215 


A  STUDY  OF   THE   RELATIVE   RELIABILITY  OF 
OFFICIAL  TESTS  OF  DAIRY  COWS 


BY  W.  W.  YAPP 


URBANA,  ILLINOIS,  FEBRUARY,  1919 


CONTENTS  OP  BULLETIN  No.  215 

PAGE 

1.  INTRODUCTION 323 

2.  EXPLANATION  OF  TESTS 323 

3.  NATURE  OF  AVAILABLE  RECORDS 324 

4.  PLAN  OF  INVESTIGATION 325 

5.  ACCURACY  OF  THE  SEMIOFFICIAL  TEST 325 

6.  RELATION  OF  FAT  PERCENTAGE  TO  TEST  PERIOD 

Seven-Day  Test  327 

Semiofficial  Test 328 

7.  VARIABILITY  IN  PERCENTAGE  OF  FAT 

Seven-Day  Test    330 

Semiofficial  Test   332 

8.  COMPARISON  OF  SEVEN-  AND  THIRTY-DAY  TESTS 333 

9.  COMPARISON  OF  SEVEN-DAY  TEST  AND  SEVEN-DAY  TEST  EIGHT  MONTHS 

AFTER  CALVING  334 

10.  CORRELATION  BETWEEN  SEVEN-DAY  AND  SEMIOFFICIAL  MILK  PRODUCTION.  337 

11.  CORRELATION  BETWEEN  SEVEN-DAY  AND  SEMIOFFICIAL  FAT  PRODUCTION.  .  338 

12.  CONCLUSIONS  .  .  339 


A   STUDY  OF  THE   RELATIVE   RELIABILITY  OF 
OFFICIAL  TESTS  OF  DAIRY  COWS 

BY  W.  W.  YAPP,  ASSOCIATE  ix  DAIRY  HUSBANDRY 

INTRODUCTION 

The  rearing  of  pure-bred  cattle  for  dairy  and  breeding  purposes 
has  developed  into  a  business  of  considerable  financial  importance,  no 
small  part  of  which  has  been  brought  about  by  the  establishment  of 
systems  of  Advanced  Registry  based  upon  milk  and  butter-fat  produc- 
tion. 

During  the  earlier  years  of  the  life  of  the  various  breed  associa- 
tions but  few  records  were  made,  and  the  supervision  of  official  test- 
ing was  essentially  a  simple  process.  During  this  period  it  was  ex- 
tremely desirable  to  have  a  test  which  was  easily  operated  and,  at  the 
same  time,  relatively  inexpensive.  The  short-time  test  seemed  to  meet 
these  requirements  satisfactorily  and  therefore  was  placed  in  service 
in  some  of  the  breed  associations. 

Thru  the  general  use  of  these  short-time  tests  the  cows,  in  at  least 
one  of  these  associations,  made  a  very  noticeable  increase  in  butter-fat 
production.  So  great  was  this  apparent  increase  that  some  breeders 
were  led  to  believe  that  a  longer  test  period  might  represent  more 
accurately  the  real  value  of  these  cows  as  producers  of  milk  and  butter 
fat.  This  feeling  spread  over  the  country  to  a  considerable  extent, 
and  it  was  with  the  idea  of  throwing  some  light  upon  the  reliability 
of  these  short-time  tests  that  the  studies  which  are  reported  herein 
were  begun. 

These  studies  are  confined  entirely  to  the  Holstein-Friesian  breed 
of  dairy  cattle,  owing  partly  to  the  fact  that  more  tests  of  this  breed 
were  available  for  comparison  and  partly  to  the  fact  that  the  Holstein- 
Friesian  Association  made  the  seven-day  test  the  basis  of  requirement 
for  entry  to  the  Advanced  Register. 

EXPLANATION  OF  TESTS 

Thruout  the  course  of  this  work  references  will  be  made  repeatedly 
to  the  different  test  periods,  the  most  important  of  which  are:  the 
seven-day  test,  the  thirty-day  test,  the  seven-day  test  eight  months 
after  calving,  and  the  semiofficial  long-time  test,  which  usually  covers 
a  yearly  period. 

The  seven-day  test  is  an  official  test1  which  covers  a  period  of  seven 

*An  official  test  is  one  in  which  the  supervisor  or  tester  weighs  and  tests  the 
milk  of  eaqh  milking  separately,  being  present  at  each  and  every  milking  during 
the  entire  testing  period. 

323 


324  BULLETIN  No.  215  [February, 

consecutive  days  and  may  be  begun  as  early  as  the  seventh  day  after 
a  cow's  last  calving.  After  satisfying  the  minimum  requirements  for 
this  test,  cows  are  admitted  to  the  Advanced  Registry  and  are  desig- 
nated -as  A.  R.  0.  cows.1  None  of  the  other  tests  named  will  be  ac- 
cepted for  publication  by  the  Advanced  Registry  unless  they  are 
made  by  A.  R.  O.,  cows.2 

The  thirty-day  test  is  one  which  covers  a  period  of  thirty  consecu- 
tive days  and  is  governed  by  essentially  the  same  rules  as  the  seven- 
day  test. 

The  seven-day  test  eight  months  after  calving  is  also  an  official  test, 
and  may  be  begun  not  less  than  eight  months  (240  days)  after  a 
cow's  last  calving.  In  order  that  this  test  be  accepted  for  publica- 
tion in  the  Advanced  Register,  it  must  be  preceded  by  a  seven-day 
test  made  during  the  same  lactation  period;  and  there  must  be  an 
interval  of  not  less  than  170  days  between  the  two  tests. 

The  semiofficial  long-time  test3  may  be  begun  not  earlier  than  the 
fourth  day  after  calving,  and  may  be  continued  during  that  period  of 
lactation  or  such  consecutive  part  of  it  as  the  owner  may  desire,  but 
it  must  not  exceed  365  days  in  length.  If  this  test  is  made  of  the 
production  of  an  A.  R.  0.  cow,  and  the  results  meet  the  established 
requirements,  the  test  is  accepted  for  publication  by  the  Advanced 
Registry. 


All  the  records  used  in  this  work  have  been  taken  from  the  Hol- 
stein-Friesian  Advanced  Register,  the  official  publication  of  the  Hol- 
stein-Friesian  Association.  In  collecting  these  data,  all  cows  and 
heifers  which  had  made  semiofficial  long-time  tests  with  comparable4 
seven-day  tests  prior  to  May  1,  1915,  were  included.  In  addition,  a 
study  was  made  of  all  the  thirty-day  tests  and  of  all  the  seven-day 
tests  eight  months  after  calving  which  had  comparable  seven-day  tests 

*The  letters  A.  R.  O.  stand  for  Advanced  Registry  Official  and  indicate  that 
the  test  was  official,  that  is,  made  under  continuous  supervision. 

SA  recent  ruling  of  the  Association  has  waived  the  seven-day  test  as  a  require- 
ment for  entry  to  the  Advanced  Registry  for  the  semiofficial  test. 

*A  semiofficial  test  is  one  in  which  the  percentage  of  fat  in  the  milk  is  de- 
termined by  an  official  test  that  covers  a  period  of  not  less  than  two  consecutive 
days  each  month.  The  approximate  fat  production  for  the  month  is  found  by 
multiplying  the  weight  of  milk  which  the  owner  supplies  by  a  number  representing 
the  percentage  of  fat  found  during  the  period  of  official  test.  The  total  fat 
production  for  the  period  is  the  sum  of  these  various  monthly  credits. 

4In  this  study  a  comparable  test  is  considered  as  one  that  is  made  by  the 
same  cow  during  the  same  lactation  period.  A  cow  might  have  a  seven-day  test 
made  as  a  two-year  old  and  a  semiofficial  test  made  at,  a  mature  cow,  but  these 
would  not  be  comparable  and  therefore  would  not  be  given  consideration  in  this 
study. 


1919]  RELATIVE  RELIABILITY  OP  OFFICIAL  TESTS  OF  DAIRY' Cows  325 

and  were  made  prior  to  May  1,  1913.  In  selecting  the  individuals 
which  possessed  semiofficial  tests,  only  those  with  records  covering  a 
period  of  330  days  or  more  were  included.  All  the  tests  used  in  this 
work  are  official  tests  except  those  designated  as  semiofficial. 

PLAN  OF  INVESTIGATION 

In  this  study  the  semiofficial  test  has  been  taken  as  the  standard 
and  has  been  used  as  the  basis  for  comparison.  After  checking  the 
accuracy  of  the  semiofficial  test,  an  attempt  has  been  made  to  deter- 
mine its  relationship  to  the  seven-day  test  with  respect  to  the  per- 
centage of  fat  which  each  carries.  The  thirty-day  test  and  the  seven- 
day  test  eight  months  after  calving  have  each  been  compared  with 
their  comparable  seven-day  tests.  To  show  the  extent  to  which  the 
seven-day  tests  may  be  used  as  an  indication  of  yearly  production, 
correlation  coefficients  have  been  calculated  for  the  seven-day  and 
the  yearly  tests,  both  for  milk  and  for  fat. 

ACCURACY  OF  THE  SEMIOFFICIAL  TEST 

It  became  evident  early  in  this  study  that  it  was  necessary  to 
establish  some  basis  of  comparison  for  the  different  records.  Natu- 
rally, the  yearly  record,  since  it  covered  a  longer  period,  suggested 
itself  as  the  standard  by  which  the  other  records  might  be  measured. 
It  was  realized,  however,  that  the  method  employed  in  determining 
yearly  production  had  been  criticized  by  some  for  its  lack  of  accuracy, 
and  it  was  decided  advisable  to  check  the  accuracy  of  this  test,  in  so 
far  as  possible. 

For  a  number  of  years,  a  daily  record,  to  which  each  milking  con- 
tributed proportionately,  has  been  kept  of  the  production  of  each 
cow  in  milk  in  the  University  herd.  A  number  of  these  cows  have 
also  made  semiofficial  records.  For  convenience,  the  test  regularly 
used  in  the  University  herd  is  designated  as  the  "continuous  test."1 

In  order  to  measure  the  relationship  between  these  two  methods 
of  testing,  the  mean,  the  standard  deviation,  and  the  coefficient  of 
variability  are  calculated  for  the  fat  production  as  obtained  by  each.2 
Tables  1  and  2  present  the  results. 


*In  the  University  herd  the  continuous  test  is  conducted  essentially  as  fol- 
lows: Each  milking  is  weighed  and  sampled.  The  sample  taken,  which  repre- 
sents an  aliquot  part  of  the  milk,  is  placed  in  a  closed  bottle  containing  a  small 
amount  of  preservative.  At  the  end  of  each  week  the  composite  thus  formed  is 
tested  for  butter  fat.  The  fat  percentage  found  is  taken  as  the  average  for  the 
week,  aqd  when  multiplied  by  a  number  representing  the  pounds  of  milk  for  that 
period,  gives  the  weekly  fat  production.  The  sum  of  these  various  weekly  pro- 
ductions constitutes  the  yearly  butter-fat  record. 

2It  is  not  necessary  to  compare  these  two  methods  of  testing  with  respect 
to  the  amount  of  milk  produced,  since  both  methods  require  that  the  milk  of  each, 
and  every  milking  be  accurately  weighed  and  recorded. 


326 


BULLETIN  No.  215 


[February, 


TABLE  1. — YEABLY  BUTTER-FAT  PRODUCTION  OF  THIRTY  Cows  IN  THE  UNIVERSITY 
HERD,  AS  ASCERTAINED  BY  THE  CONTINUOUS  TEST 


Class  interval  ; 
fat  production, 
Ibs. 

Frequency 

Average 
deviation 

F(AD) 

F(AD)  ' 

250—300 
301—350 
351^400 
425.5    401—450 

1 
3 
9 
10 
3 
3 
1 

-3 
-2 
-1 
0 

+1 
+2 
+3 

-3 

-6 
-9    -18 
0 

+3 
+6 
+3  +12 

9 
12 
9 
0 
3 
12 
9 

50      451—500 
501—550 
551—600 

30 

-6 

54 

Mean :    425  —  10.00  =  415.50  ±  8.12 
Standard  deviation:    66.1  ±  5.76 
Coefficient  of  variability:     15.90  ±  1.38 

TABLE  2. — YEARLY  BUTTER-FAT  PRODUCTION  OF  THIRTY  Cows  IN  THE  UNIVERSITY 
HERD,  AS  ASCERTAINED  BY  THE  SEMIOFFICIAL  TEST 


Class  interval; 
fat  production, 
/6s. 

Frequency 

Average 
deviation 

F(AD) 

F(AD)2 

251—300 
301*—  350 
351—400 
425.5     401—450 

1 
4 
10 
8 
4 
2 
1 

_g 

-2 
-1 
0 

+1 
+2 
4-3 

-3 

-8 
-10    -21 
0 

+4 
+4 
+3  +11 

9 
16 
10 
0 
4 
8 
9 
56 

50      451—500 
501—550 
551—600 

30 

-10 

Mean :    425.5  —  16.65  =  408.85  ±  8.14 
Standard  deviation:    66.25  ±  5.77 
Coefficient  of  variability:    16.20  ±  1.41 

From  a  study  of  these  tables  it  is  observed  that  the  mean,  or 
average,  production  of  the  cows  when  making  the  continuous  test  was 
415.5  pounds  of  fat  ±  8.1  pounds;  whereas  the  semiofficial  test  of 
the  production  of  the  same  cows  during  the  same  period  shows  408.9 
pounds  Hh  8.1.  This  slight  difference  between  the  averages  shown  by 
the  two  different  methods  of  testing  is  not  regarded  as  significant. 

The  standard  deviation  in  the  case  of  the  continuous  test  is  66.1 
±  5.8 ;  while  that  for  the  semiofficial  is  66.25  ±  5.8.  Again  there  is 
a  rather  unusually  close  relationship  between  the  two  methods  of  test- 
ing. The  coefficient  of  variability  in  the  case  of  the  continuous  test 
is  15.90  Hh  1.38  percent;  whereas,  in  the  case  of  the  semiofficial  test, 
it  is  16.20  ±  1.41  percent,  a  difference  that  is  not  significant. 

These  data  are  not  held  to  be  comprehensive,  but  so  far-  as  the 
limited  number  of  records  involved  can  be  used  to  indicate  the  rela- 
tion between  the  two  tests,  they  seem  to  indicate  very  little  difference. 


1919} 


RELATIVE  RELIABILITY  OF  OFFICIAL  TESTS  OF  DAIRY  Cows 


327 


These  data  support  the  general  opinion  that  the  semiofficial  test  is 
a  fairly  accurate  measure  of  the  producing  ability  of  cows. 

RELATION  OF  FAT  PERCENTAGE  TO  TEST  PERIOD 

SEVEN-DAY  TEST 

In  the  study  of  the  percentage  of  fat  in  the  milk  during  these 
various  test  periods,  it  is  necessary  to  deal  in  averages.  Table  3  shows 
the  variation  in  fat  percentage  between  low  and  high  fat  production 
for  the  seven-day  test.  The  data  are  presented  graphically  in  Fig.  1. 

TABLE  3. — SEVEN-DAY  TEST:     RELATION  BETWEEN  AMOUNT  OF  FAT  AND 
PERCENTAGE  OF  FAT 


Class  interval; 
fat  production 

Frequency 

Milk 
production 

Fat  test 

Fat 
production 

Ibs. 

Ibs. 

percent 

Ibs. 

Under  9.  00 

28 

268.4 

3.14 

8.415 

9.01—12.00 

192 

318.5 

3.36 

10.697 

12.01—15.00 

350 

381.0 

3.53 

13.441 

15.01—18.00 

374 

453.1 

3.64 

16.479 

18.01—21.00 

214 

503.3 

3.84 

19.325 

21.01—24.00 

114 

574.6 

3.97 

22.837 

24.01—27.00 

18 

587.1 

4.26 

25  .  025 

27.01  and  over 

4 

567.5 

5.15 

29.226 

From  this  study  of  the  seven-day  test  it  is  shown  that  low  fat 
production  is  accompanied  by  a  correspondingly  low  fat  percentage, 
and  high  fat  production  accompanied  by  a  relatively  high  fat  per- 
centage. Individuals  that  produced  on  the  average  8.415  pounds  of 
fat  for  the  seven-day  period  produced  milk  having  an  average  fat 


54 


34 


7 


16  IS  20 

LBS.  FftT 


26  28 


1. — SEVEN-DAY  TEST:   RELATION  BETWEEN  AMOUNT  OF  FAT  AND  PERCENTAGE 

OF  FAT 


328 


BULLETIN  No.  215 


[February, 


test  of  3.14  percent;  whereas  those  producing  an  average  of  25.025 
and  29.226  pounds  of  fat  for  the  same  period  produced  milk  having 
an  average  fat  test  of  4.26  and  5.15  percent,  respectively ;  the  differ- 
ence between  the  lowest  and  the  highest  group  in  percentage  of  fat 
being  2.01  percent.  Not  only  is  the  increase  in  the  amount  of  fat 
produced,  accompanied  by  a  corresponding  increase  in  the  percentage 
of  fat,  but  there  is  also  an  increase  in  milk  production,  tho  not  in 
proportion  to  the  fat  increase. 

One  of  the  noticeable  features  of  the  curve  shown  in  Fig.  1  is  its 
smoothness,  there  being  a  tendency  for  it  to  rise  uniformly  with  the 
increase  in  fat  production.  This  fact  indicates  that  high  butter-fat 
records  for  the  seven-day  period  are  secured,  to  a  rather  high  degree, 
by  high  fat  tests  rather  than  by  unusually  heavy  milk  production. 

SEMIOFFICIAL  TEST 

Table  4  and  Fig.  2  show  the  relation  between  amount  of  fat  and 
percentage  of  fat  as  recorded  under  the  semiofficial  test. 

TABLE  4. — SEMIOFFICIAL  TEST:     RELATION  BETWEEN  AMOUNT  OF  FAT  AND 
PERCENTAGE  OF  FAT 


Class  interval; 
fat  production 

Frequency 

Milk 
production 

Fat  test 

Fat 
production 

Ibs. 

lb*. 

percent 

Ibs. 

251—350 

83 

9583.7 

3.35 

320.585 

351—450 

349 

12  100.6 

3.35 

405.382 

451—550 

410 

14747.0 

3.39 

499.977 

551—650 

270 

17  142.1 

3.47 

595.983 

651—750 

122 

19875.9 

3.48 

691.735 

751—850 

35 

21  720.8 

3.62 

787.161 

851—950 

16 

24  453  .  3 

3.65 

892  .  332 

951—1050 

9 

26  225  6 

3.79 

993.367 

1051—1150 

1 

24612.8 

4.53 

1  116.050 

A  study  of  this  table  shows  that  under  the  semiofficial  test  there 
is  a  difference  between  the  fat  percentage  of  low  butter-fat  production 
and  that  of  high  butter-fat  production,  but  this  difference  is  not  nearly 
so  great  as  in  the  case  of  the  seven-day  test.  In  the  semiofficial  test, 
low  butter-fat  production  is  not  accompanied  by  an  extremely  low 
fat  percentage  nor  is  high  butter-fat  production  accompanied  by  an 
extremely  high  fat  percentage.  In  low  production  (320.585  pounds 
of  fat  for  the  yearly  period)  the  average  percentage  of  fat  was  3.35 ; 
whereas  in  high  production  (993.3671  pounds  of  fat  for  the  same 
period)  the  average  percentage  of  fat  was  3.79,  a  variation  in  fat  test 
between  low  and  high  production  of  only  0.44  percent. 

lrThe  last  group,  in  which  the  variation  is  between  1,051  and  1,150  pounds  of 
fat,  is  not  considered. 


1919 
54 

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]             RELATIVE  RELIABILITY  OF  OFFICIAL  TESTS  OF  DAIRY  Cows 

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50         325          40O         475           55O          6*5         TOO     •    7TS          OSO         Off          1000         tors        lit 

329 


AVERrtbE  LB3.  FflT 

FIG.  2. — SEMIOFFICIAL  TEST:     RELATION  BETWEEN  AMOUNT  OF  FAT  AND 
PERCENTAGE  OF  FAT 


The  curve  in  Fig.  2  shows  a  tendency  to  rise,  but  the  rise  is  much 
less  marked  than  in  the  case  of  the  curve  in  Fig.  1.  The  tendency 
in  the  semiofficial  test  seems  to  be  to  secure  high  fat  production  by 
means  of  an  increased  milk  production  rather  than  thru  a  very  high 
fat  percentage.  The  difference  in  the  results  from  these  two  tests  is 
brought  out  more  clearly  when  the  two  curves  are  superimposed  upon 
the  same  graph.  This  is  possible  since  both  curves  are  drawn  to  the 
same  scale.  Fig.  3  shows  this  relationship. 


FIG.  3. — COMPARISON  OF  SEVEN-DAY  AND  SEMIOFFICIAL  TESTS  WITH  RESPECT  TO 
THE  RELATION  BETWEEN  AMOUNT  OF  FAT  AND  PERCENTAGE  OF  FAT 


330  BULLETIN  No.  215  [February, 

These  curves  correspond  very  closely  in  fat  percentage  in  the  case 
of  low  butter-fat  production.  As  the  production  increases,  however, 
there  is  a  tendency  for  the  curves  to  separate,  with  the  seven-day  test 
showing  the  higher  percentage  of  fat.  The  difference  between  the 
two  is  greatest  in  the  case  of  high  butter-fat  production,  the  maximum 
difference  being  as  great  as  .47  percent. 

VARIABILITY  IN  PERCENTAGE  OF  FAT 

Not  only  is  the  percentage  of  fat  for  the  seven-day  test  higher  than 
that  for  the  semiofficial  period,  but  it  is  also  much  more  variable. 
Fig.  4  shows  this  variability. 

The  seven-day  test,  it  will  be  noted,  carries  not  only  a  high  aver- 
age fat  percentage,  but  in  a  number  of  single  cases  the  fat  tests  are 
exceptionally  high.  The  spread  of  the  curve  which  represents  the 
fat  percentage  for  the  seven-day  test  indicates  considerably  more 
variability  than  is  shown  by  the  semiofficial  test.  The  curve  repre- 
senting the  percentage  of  fat  for  the  semiofficial  test  indicates  that 
there  is  variability  but  that  the  variability  is  less  than  in  the  preced- 
ing case.  This  curve  is  nearly  symmetrical  in  form  and  approximates 
what  is  called  the  normal  probability  curve. 

Altho  these  curves  show  that  there  is  a  certain  variability  in 
fat  percentage,  they  do  not  measure  this  variability.  To 'determine 
the  variability  within  each  of  these  tests,  standard  deviations  and 
coefficients  of  variability  have  been  calculated. 

SEVEN-DAY  TEST 

Table  5  shows  the  variability  in  fat  percentage  for  the  seven-day 
test.  It  is  observed  that  the  mean,  or  average,  fat  percentage  for  the 
1,295  records  considered  is  3.679  ±  0.01.  This  percentage  is  not  re- 
garded as  high  for  a  single  individual  or  a  small  group  of  selected 
individuals  of  the  Holstein-Friesian  breed,  but  it  is  considered  high 
for  a  large  and  fairly  representative  group.  The  small  probable  error 
of  ±  0.01  indicates  that  the  records  of  the  1,295  cows  considered  were 
adequate  to  determine  relatively  accurately  the  average  percentage 
of  fat  produced  by  the  class  of  cows  that  have  completed  seven-day 
records.  Altho  the  mean  gives  a  satisfactory  measure  of  the  average 
fat  percentage  for  all  cows  of  the  class  that  have  completed  seven- 
day  tests,  it  does  not  give  any  idea  as  to  whether  or  not  some  of  the 
cows  produced  milk  exceptionally  high  or  exceptionally  low  in  per- 
centage of  fat. 

The  standard  deviation,  on  the  other  hand,  describes  this  varia- 
bility. For  the  seven-day  test  we  find  a  standard  deviation  of  .5256  ± 
.007.  This  is  regarded  as  a  fairly  high  degree  of  variability.  The 
coefficient  of  variability,  14.29  ±  .18  percent,  gives  the  same  general 
result. 


1919] 


RELATIVE  RELIABILITY  OF  OFFICIAL  TESTS  OF  DAIRY  Cows 


331 


332 


BULLETIN  No.  215 


[February, 


TABLE  5. — SEVEN-DAY  TEST:    VARIABILITY  IN  FAT  PERCENTAGE 


Class  interval; 
fat  test,  percent 

Frequency 

Average 
deviation 

F(AD) 

F(AD)2 

2.21—2.40 

0 

0 

0 

0 

2.41—2.60 

4 

-6 

-24 

144 

2.61—2.80 

22 

-5 

-110 

550 

2.80—3.00 

76 

-4 

-304 

1  216 

3.01—3.20 

119 

-3 

-357 

1  071 

3.21—3.40 

178 

-2 

-356 

712 

3.41—3.60 

217 

-1 

-217  -1  368 

217 

3.705 

3.61—3.80 

223 

0 

0 

0 

.2 

3.81—4.00 

161 

1 

161 

161 

4.01—4.20 

118 

2 

236 

472 

4.21—4.40 

80 

3 

240 

720 

4.41—4.60 

33 

4 

132 

528 

4.61—4.80 

26 

5 

130 

650 

4.81—5.00 

13 

6 

78 

468 

5.01—5.20 

5 

7 

35 

245 

5.21—5.40 

8 

8 

64 

512 

5.41—5.60 

4 

9 

36 

324 

5.61—5.80 

3 

10 

30 

300 

5.81—6.00 

4 

11 

44 

484 

6.01—6.20 

0 

12 

0 

0 

6.21—6.40 

0 

13 

0 

0 

6.41—6.60 

1 

14 

14+1  200 

196 

• 

1295 

-  168 

8970 

Mean:     3.679  ±  .010 

Standard  deviation:    0.5256  ±   .0069 

Coefficient  of  variability:    14.29  ±  .18 

SEMIOFFICIAL  TEST 

The  calculation  of  the  mean,  the  standard  deviation,  and  the  co- 
efficient of  variability  for  the  semiofficial  test  furnishes  an  added  op- 
portunity for  comparison.  Table  6  shows  the  variability  in  percentage 
of  fat  for  the  semiofficial  test. 

The  mean,  or  average  percentage  of  fat,  for  the  semiofficial  period 
is  3.43  ±  .006  percent.  It  is  true  that  this  average  test  is  based  on 
a  rather  selected  group  of  cows;  but  the  probable  error  (±  .006) 
indicates  that  this  group  of  1,295  is  adequate  to  determine  a  reliable 
average  percentage  of  fat  for  the  class  of  cows  making  semiofficial 
tests.  The  standard  deviation  of  .317  ±  .004  indicates  that  there  is 
variability,  but  this  variability  is  not  so  great  as  that  found  in  the 
case  of  the  seven-day  test,  the  coefficient  of  variability  being  9.22  ±  .12. 

In  fat  percentage  the  seven-day  test  is  more  variable  than  the  semi- 
official, the  difference  between  the  two  tests  being  quite  significant. 
This  fact  is  of  importance  to  the  breeder  who  is  forced  to  make  selec- 
tions from  cows  with  seven-day  records  when  he  desires  to  breed  up 
a  herd  in  which  the  individuals  have  a  higher  percentage  of  fat  in 
their  milk  for  longer  periods. 


1 919}  EELATIVE  RELIABILITY  OP  OFFICIAL  TESTS  OF  DAIRY  Cows  333 

TABLE  6. — SEMIOFFICIAL  TEST:    VARIABILITY  IN  FAT  PERCENTAGE 


Class  interval; 
fat  test,  percent 

Frequency 

Average 
deviation 

F(AD) 

F(AD)2 

2.21—2.40 
2.41—2.60 
2.61—2.80 
2.81—3.00 
3.01—3.20 
3.305    3.21—3.40 

1 
2 
14 
65 
213 
333 
329 
205 
78 
29 
15 
10 
0 
1 

-5     • 
-4 
-3 
-2 
-1 
0 
1 
2 
3 
4 
5 
6 
7 
8 

-5 
-8 
-42 
-130 
-213        -398 
0 
329 
410 
234 
116 
75 
60 
0 
8  +1  232 

25 
32 
126 
260 
213 
0 
329 
820 
702 
464 
375 
360 
0 
64 

.2        3.41—3.60 
3.61—3.80 
3.81—4.00 
4.01—4.20 
4.21—4.40 
4.41—4.60 
4.61—4.80 
4.81—5.00 

1  295 

+  834 

:j  770 

Mean :    3.434  ±  .006 

Standard  deviation:    .3166  ±  .004 

Coefficient  of  variability :    9.22  ±  .12 


COMPARISON  OF  SEVEN-  AND  THIRTY-DAY  TESTS 

Many  breeders  are  continuing  their  cows  on  official  test  for  a 
thirty-day  period.  Naturally  they  are  interested  in  knowing  how  it 
compares  with  the  seven-day  test.  Table  7  and  Fig.  5  show  the  rela- 
tion between  the  seven-day  and  the  thirty-day  tests  with  respect  to 
fat  percentage. 

TABLE  7. — COMPARISON  OF  SEVEN-  AND  THIRTY-DAY  TESTS 


Seven-day  test 

Fre- 
quency 

Thirty-day  test 

Milk 
production 

Fat  test 

Fat  pro- 
duction 

Milk 
production 

Fat  test 

Fat  pro- 
production 

/6s. 
246.8 
330.2 
394.5 
465.7 
528.3 
580.6 

percent 
3.41 
3.29 
3.45 
3.59 
3.66 
4.05 

Ibs. 
8.415 
10.853 
13.623 
16.702 
19.692 
23.534 

4 
74 
216 
372 
349 
375 

Ibs. 
1  021.8 
1  367.3 
1640.9 
1  937.5 
2238.0 
2445.0 

percent 
3.32 
3.19 
3.33 
3.45 
3.52 
3.80 

Ibs. 
33.907 
44.362 
54.691 
66.762 
78.578 
92  .  997 

In  this  comparison  between  seven-  and  thirty-day  tests,  the  records 
are  arranged  in  groups  according  to  seven-day  production.  With  this 
arrangement  there  may  be  a  tendency  for  the  thirty-day  test  to  re- 
gress toward  the  mean  fat  percentage  for  cows  in  general,  but  when 
it  is  considered  that  in  almost  every  case  the  seven-day  test  forms 
a  part  of  the  thirty-day  period,  it  is  apparent  that  the  tendency  to 
regress  must  be  slight. 


334 


BULLETIN  No.  215 


[February, 


The  curves  in  Fig.  5  show  that  there  is  a  uniform  difference  be- 
tween these  two  tests  with  respect  to  the  percentage  of  fat  found  in 
the  milk.  This  comparison,  based  on  an  aggregate  of  1,390  individual 
records,  shows  the  seven-day  test  to  have  the  higher  percentage  of  fat. 
The  difference  in  fat  percentage  between  the  tests  is  greatest  in  the 
case  of  high  production.  In  low  production  the  variation  is  .1  percent 
of  fat;  in  high  production,  .25  of  fat;  making  a  difference  of  .15 
percent  between  the  extremes. 


40 


58 


50 


TrtJRTT-PAY  TEST 


,10 


16  IS 

rtVERASEL  LBS.  PrtT 


FIG.  5. — COMPARISON  OF  SEVEN-DAY  AND  THIRTY-DAY  TESTS  WITH  EESPECT  TO 

PERCENTAGE  OF  FAT 

The  drop  in  the  curve  in  low  production  may  be  due  to  the  fact 
that  only  four  individual  records  are  included  in  the  averages  which 
constitute  the  first  group.  Generally  speaking,  this  number  of  rec- 
ords would  be  insufficient  to  establish  dependable  results. 


COMPARISON  OF  THE  SEVEN-DAY  TEST  AND  THE  SEVEN- 
DAY  TEST  EIGHT  MONTHS  AFTER  CALVING 

The  seven-day  test  eight  months  after  calving  has  evidently  been 
little  favored  by  breeders  of  Holstein-Friesian  cattle,  as  only  209  tests 
were  available  for  comparison  prior  to  May  1,  1913.  Table  8  shows 
the  average  fat  percentage  of  the  various  groups  for  the  original  seven- 
day  test  when  arranged  according  to  amount  of  fat  production,  and 
Table  9  shows  the  same  for  the  seven-day  test  eight  months  after 
calving.  For  graphic  presentation,  see  Figs.  6  and  7. 


1919} 


RELATIVE  RELIABILITY  OF  OFFICIAL  TESTS  OF  DAIRY  Cows 


335 


TABLE  8. — ORIGINAL  SEVEN-DAY  TEST:     RELATION  BETWEEN  FAT  PRODUCTION 

AND  FAT  TEST 


Class  interval; 
fat  production 

Frequency 

Milk 
production 

Fat  test 

Fat 
production 

/6s. 
Under      9  .  00 
9.01—12.00 
12.01—15.00 
15.01-18.00 
18.01—21.00 
21  .  01  and  over 

4 
32 
55 
58 
39 
21 

/6s. 
261.1 
316.7 
383.7 
450.0 
515.8 
593.8 

percent 
3.15 
3.38 
3.48 
3.67 
3.76 
4.08 

/6s. 
8.236 
10.698 
13.366 
16.531 
19.379 
24.246 

TABLE  9. — SEVEN-DAY  TEST  EIGHT  MONTHS  AFTER  CALVING: 
BETWEEN  FAT  PRODUCTION  AND  FAT  TEST 


RELATION 


Class  interval; 
fat  production 

Frequency 

Milk 
production 

Fat  test 

Fat 
production 

/6s. 
Under    8.00 
8.01—10.00 
10.01—12.00 
12.01—14.00 
14.01—16.00 
16.01—18.00 
18.01  and  over 

30 
69 
59 
33 
11 
6 
1 

/6s. 
211.1 
262.5 
305.9 
359.5 
401.0 
423.5 
492.1 

percent 
3.28 
3.46 
3.62 
3.62 
3.68 
3.78 
4.31 

/6s. 
6.925 
9.085 
11.084 
12.987 
14.749 
15.993 
21  .  195 

From  a  study  of  these  tables  and  curves  it  is  evident  that  there 
is  a  slight  difference  between  the  two  tests  in  low  fat  production ;  the 
seven-day  test  eight  months  after  calving  being  slightly  higher  in  fat 
percentage  than  the  original  seven-day  test.  In  the  case  of  those  cows 
which  averaged  10.698  pounds  of  fat  for  the  original  seven-day  test, 
the  average  fat  percentage  was  3.38;  whereas  cows  that  averaged 
9.085  pounds  fat  when  tested  for  seven  days  eight  months  after 
calving,  had  an  average  fat  percentage  of  3.46. 

In  high  average  fat  production  the 'reverse  is  true,  the  original 
seven-day  test  having  the  higher  fat  percentage.  Those  cows  which 
averaged  24.246  pounds  of  fat  for  the  original  seven-day  test  pro- 
duced, on  the  average,  milk  testing  4.08  percent.  On  the  other  hand, 
cows  producing  an  average  of  15.993  pounds  of  fat  in  the  seven-day 
test  eight  months  after  calving,  produced  milk  which  on  the  average 
tested  but  3.78  percent ;  there  being  a  greater  difference  between  the 
two  tests  in  the  percentages  representing  high  average  fat  production 
than  in  the  percentages  representing  low  average  fat  production. 

In  this  comparison,  it  must  be  borne  in  mind  that  a  relatively  small 
number  of  records  are  involved,  and  therefore  that  too  much  signifi- 
cance should  not  be  attached  to  the  results. 


336 


BTTLTETTN  No.  215 


[February? 


PERCENT  Or  POT 

_g  ft  fc  ft  85  i  ft  i 

ORISINftl 

.  SEVEN- 

J>ftY  TEST 

ft 

^ 

/ 

X 

x^ 

^^e" 

^ 

^^ 

7 

/ 

s* 

7 

5            10            12            14            16            id           20          22           24           2 

AVERAGE  LBS.    FftT 

FIG.  6. — ORIGINAL  SEVEN-DAY  TEST:     EELATIOX  BETWEEN  AMOUNT  OF  FAT  AND 

PERCENTAGE  OF  FAT 


PERCENT  or  r«r 
§  K  S  «  &  *  *  j 

o 

SEV 

EN-^flY 

TEST  EK 

pOTOOMK 

»S  ftREF 

CflLVtNG 

^ 

X 

/ 

S 

X 

)0 


20 


FIG.  7. — SEVEN-DAY  TEST  EIGHT  MONTHS  AFTER  CALVING:     RELATION  BETWEEN 
AMOUNT  OF  FAT  AND  PERCENTAGE  OF  FAT 


1919] 


RELATIVE  RELIABILITY  OF  OFFICIAL  TESTS  OF  DAIRY  Cows 


337 


CORRELATION  BETWEEN  SEVEN-DAY  AND  SEMI- 
OFFICIAL MILK  TESTS 

The  measurement  of  correlation  in  this  study  has  been  confined 
to  seven-day  and  semiofficial  tests.  The  popularity  and  extensive  use 
of  the  seven-day  test  makes  it  extremely  desirable  that  the  extent  to 
which  it  may  be  used  as  an  indication  of  semiofficial  production,  be 
determined.  To  measure  the  relationship  which  exists  between  these 
two  tests,  correlation  tables  have  been  used  and  coefficients  have  been 
determined. 

TABLE  10. — CORRELATION  BETWEEN  SEVEN-DAY  AND  SEMIOFFICIAL  MILK 

PRODUCTION 

Semiofficial  Milk  Production 


Class 
interval; 

lg 

1 

l,| 

(s 

| 

i 

I 

, 

I 

i 

j 

production, 
Ibs. 

<-<o 

S05 

§1—  i 
^H 

OCO 

i—  i  r—  i 

oo 

O  iO 

CO  l-H 

oo 

iO  i—  1 

t>  i-t 

C5<N 

oo 
oeo 

i-H  (M 

CO  C^ 

o  t> 
»oc^ 

O    Oi 

tXM 

§pH 
CO 

jj 

Ja 

ft 

201—250 

7 

fi 

4 

17 

251  —  300 

11 

33 

34 

13 

1 

92 

301—350 

6 

35 

73 

43 

14 

2 

1 

174 

351—400 
401—450 
451—500 
501—550 
551—600 
601—650 
651—700 
701  —  750 

3 

1 

20 
8 
4 
1 

70 
45 
31 
8 
3 

70 
80 
51 
22 
5 
2 

47 
82 
46 
33 
23 
4 
1 

14 
39 
47 

48 
25 

7 
2 

2 
14 
17 
27 
17 
8 
1 
1 

1 
3 
6 
16 
11 
10 
2 

i 
i 

3 
1 
6 
2 

i 

'i 
'?, 

i 

i 

2 
1 

i 

'i 
i 

227 
274 
203 
158 
87 
42 
11 
5 

751—800 

1 

a 

1 

4 

801—850 

0 

851—900 

0 

901—950 

1 

1 

Total  

28 

107 

268 

286 

251 

184 

88 

50 

16 

7 

7 

3 

1295 

Table  10  shows  the  distributions  from  which  the  coefficient  of  cor- 
relation for  the  seven-day  and  the  semiofficial  milk  production  rec- 
ords has  been  calculated.  A  study  of  the  results  shows  that  there  is 
a  coefficient  of  correlation  of  .702  ±  .01  between  the  seven-day  and 
the  semiofficial  tests.  The  correlation  .702  is  for  certain  purposes  a 
high  degree  of  correlation,  but  it  is  not  a  high  degree  of  correlation 
between  two  measurements  of  the  same  thing.  That  is  to  say,  we  are 
here  concerned  with  two  methods  of  measuring  milk  production  of 
the  same  cow,  and  in  order  that  each  of  them  may  be  an  effective 
measure  of  this  production,  they  ought  to  be  more  closely  correlated. 


333 


BULLETIN  No.  215 


[February, 


CORRELATION  BETWEEN  SEVEN-DAY  AND  SEMI- 
OFFICIAL FAT  PRODUCTION 

In  a  similar  way  the  coefficient  of  correlation  between  seven-day 
and  semiofficial  fat  production  has  been  determined.  Table  11  gives 
the  distribution  from  which  this  correlation  has  been  calculated.  From 
this  table  we  find  that  the  coefficient  of  correlation  of  fat  production 
between  the  seven-day  and  the  semiofficial  tests  is  .703  ±  .01,  practi- 
cally the  same  as  that  found  for  milk  production ;  but,  as  in  the  case 
of  milk  production,  altho  it  is  a  high  correlation  for  certain  purposes, 
it  is  not  so  regarded  in  this  instance  since  the  two  tests  are  supposed 
to  measure  the  same  thing. 

TABLE  11. — CORRELATION  BETWEEN  SEMIOFFICIAL  AND  SEVEN-DAY  FAT 

PRODUCTION 

Semiofficial  Fat  Production 


d 

0 

'•§ 

_  Class 
interval  ; 
fat 
production, 
Ibs. 

IO 
—I  <M 
«CM 
M 

lo 

COO 
IM-* 

co 

Ijg 
i—  10 

O-* 

5 

is 

o  >o 
JK 

U3 

!-H  <N 

<OCO 

>O 

coS 

(MO 

CO 

Ig 

3£ 
o 

lo 

CO  lO 
000 

o 

»c 

I-H  CN 
ICO 
00 

I2 

U3 

r-lO 

SO 
I—  1 

1—  1 

lo 

CO  10 

O  rH 

Oi-* 

i-H 

3 
& 

a 
*& 

7.01—  9.00 

IS 

9 

6 

31 

0 

9.01—11.00 

14 

61 

33 

6 

1 

115 

An 
t» 

11.01—13.00 
13.01—15.00 

5 
3 

63 
4? 

71 

78 

41 

80 

9 
29 

6 

1 

V.   . 

190 
238 

Seven-Day  F? 

15.01—17.00 
17.01—19.00 
19.01—21.00 
21.01—23.00 
23.01—25.00 
25.01—27.00 
27.01—29.00 
29.01—31.00 

15 
8 
1 
1 

64 
37 
9 
5 
2 

78 
51 
24 
14 
6 
] 

57 
55 
36 
17 
6 
1 
1 

24 
45 
32 
16 
8 
2 

10 
12 
16 
11 
5 
1 
1 

1 

3 

2 
5 

7 
4 

1 

1 
1 

4 
4 
3 

i 

1 

'fi 

2 
1 

1 
'i 

'i 

249 
212 
122 
73 
44 
14 
3 
4 

Total.  . 

38 

200 

305 

301 

212 

133 

57 

23 

14 

9 

2 

i 

1295 

From  this  study  of  correlation  it  would  seem  that  it  makes  little 
difference  whether  one  considers  milk  production  or  fat  production, 
since  the  coefficients  of  correlation  in  both  cases  are  almost  the  same. 
It  further  follows  that  since  the  correlation  between  seven-day  and 
semiofficial  tests  is  not  high,  it  is  not  safe  to  attempt  to  use  the  seven- 
day  as  a  criterion  by  which  to  judge  semiofficial  production. 


1919]  RELATIVE  RELIABILITY  OP  OFFICIAL  TESTS  OF  DAIRY  Cows  339 

CONCLUSIONS 

From  the  data  presented  the  following  conclusions  seem  war- 
ranted. Of  course,  since  they  are  based  on  the  average  of  a  large 
number  of  records,  it  must  be  remembered  that  they  do  not  neces- 
sarily apply  to  individual  cases. 

1.  The  semiofficial  test  represents  fairly  accurately  the  produc- 
ing ability  of  cows. 

2.  There  is  a  greater  difference  in  fat  percentage  between  low 
and  high  fat  production  shown  by  the  seven-day  test  than  by  the  semi- 
official test. 

3.  There  is  a  greater  tendency  for  high  fat  percentage  to  accom- 
pany high  fat  production  in  the  seven-day  test  than  in  the  semiofficial 
test. 

4.  The  variability  in  fat  percentage  is  greater  for  the  seven-day 
test  than  for  the  semiofficial  test.    In  fact  the  difference  between  these 
two  tests  is  quite  significant. 

5.  The  seven-day  test  shows  a  higher  percentage  of  fat  than  the 
thirty-day  test.     The  difference  is  most  marked  in  high  production. 

6.  The  limited  number  of  records  available  for  comparison  indi- 
cate that  the  seven-day  test  eight  months  after  calving  carries  a  higher 
fat  percentage  in  low  fat  production  and  a  lower  fat  percentage  in 
high  fat  production  than  the  seven-day  test. 

7.  The  correlation  between  seven-day  and  semiofficial  tests  is  not 
high  either  in  milk  or  in  fat  production,  when  it  is  considered  tliat 
they  are  measurements  of  the  same  thing. 

8.  The  data  presented  in  this  study  indicate  that  the  seven-day 
test  is  not  a  satisfactory  criterion  by  which  to  judge  semiofficial 
production, 


UNIVERSITY  OF  ILLINOIS-URBANA 


